shellRadius
plain-language theorem explainer
shellRadius assigns the k-th solvation shell radius to phi raised to the power k. Aqueous chemistry models that treat hydration layers as a geometric sequence with common ratio phi cite this definition when proving positivity or ratio properties. The definition consists of a direct power assignment with no additional lemmas.
Claim. The radius of the k-th solvation shell is given by $r_k = phi^k$, where phi is the golden-ratio fixed point.
background
The Solvation Shells from configDim module treats an ionic solute in water under configuration dimension D = 5. It enumerates five canonical shells: primary hydration, secondary hydration, tertiary hydration, bulk-boundary layer, and far bulk. Shell radii are required to lie on the phi-ladder so that the ratio of adjacent shells equals phi.
proof idea
The declaration is a direct definition that sets shellRadius k equal to phi ^ k. No lemmas or tactics are invoked; the body is the power expression itself.
why it matters
This definition supplies the explicit phi-ladder form required by SolvationShellCert and by the ratio theorem shellRadius_ratio. It realizes the geometric progression demanded by the Recognition Science phi-ladder for solvation when configDim equals 5, consistent with T6 forcing of phi as the self-similar fixed point. Downstream results in AtomicRadii then combine the radii with screening factors to produce atomic-radius proxies.
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